Thatch and moss can be treated at this time of year with physical removal, opening up the turf to air, water and the application of any granular nutrients (though also weed seeds so beware). Moss is best combated by developing the health and vigour of your grass sward, so after physically removing the moss (rake/scarify) feed the grass then re-seed any bare patches. Choose a suitable species of grass that will flourish in your prevailing conditions.
Top-dress & Over-seed
Spring and/or autumn are the traditional season for repairing bare patches and improving soil structure – essentially because any seedlings will be watered with the seasonal rainfall. In which case summer probably works as well.
The major nutrient requirements of grasses are generally of a nitrogen: phosphate: potassium ratio of NPK 2:1:1 so steer clear of those feeds that are high in nitrogen, over-stimulating top-growth and leading to a number of problems later on.